Nucleon Structure from Basis Light-Front Quantization : Status and Prospects

TL;DR

This work reviews Basis Light-Front Quantization (BLFQ) as a nonperturbative, relativistic framework for nucleon structure, detailing progress from a valence $|qqq\rangle$ sector with confinement and one-gluon exchange to including a dynamical gluon and sea-quark sectors, and finally to solving the QCD Hamiltonian without an explicit confining potential. The BLFQ approach yields nucleon light-front wavefunctions that enable predictions of electromagnetic and axial form factors, PDFs, GPDs, and TMDs, with qualitative agreement to experimental data and global analyses; it also reveals insights into orbital angular momentum and twist-3 structures, highlighting the role of higher Fock sectors. A key milestone is the emergence of nucleon LFWFs as eigenstates of the QCD Hamiltonian in a truncated basis, and the ongoing push toward Full BLFQ, where basis regulators alone would suffice to solve QCD nonperturbatively. The work emphasizes emergent hadronic mass (EHM) and outlines future directions including more complete Fock sectors, scale-dependent renormalization, and the potential of exascale computing and quantum simulations to realize a fully ab initio description of nucleon structure within BLFQ.

Abstract

We review recent advancements in understanding nucleon structure within the Basis Light-Front Quantization (BLFQ) framework--a fully relativistic, nonperturbative approach to solving quantum field theories. In its initial phase, we start with the leading Fock sector $|qqq\rangle$ and an effective light-front Hamiltonian incorporating confinement and one-gluon exchange within which BLFQ can already successfully describe key nucleon observables. The framework has since been extended to include the next-to-leading Fock sector $|qqqg\rangle$, enabling studies of gluonic contributions to the nucleon's internal structure, including gluon helicity, orbital angular momentum, and three-dimensional imaging through generalized and transverse momentum dependent parton distributions (GPDs and TMDs). Most recently, BLFQ has achieved a significant milestone by computing nucleon light-front wavefunctions as eigenstates of the QCD Hamiltonian without an explicit confining potential. These calculations, including Fock sectors up to $|qqqq\bar{q}\rangle$, further develop the path to first-principles predictions of quark and gluon matter densities, helicity and transversity distributions, and spin observables, showing qualitative agreement with experimental and phenomenological results. Together, these developments highlight BLFQ's growing capacity to provide an increasingly complete and realistic picture of nucleon structure grounded in QCD.

Figures (15)

• Figure 1: Overview of recent advances in applying BLFQ to nucleon structure studies with different Fock-sector components, including calculations of FFs, PDFs, GPDs, TMDs, and other key observables.
• Figure 2: Probability distributions of the dominant Fock sectors in the proton, as determined from our BLFQ calculations.
• Figure 3: Proton electromagnetic FFs computed using LFWFs from the leading three Fock sectors: $|qqq\rangle$, $|qqqg\rangle$, and $|qqqq\bar{q}\rangle$ as reported in Ref. Xu:2024sjt. The black lines show our BLFQ predictions, with red bands reflecting uncertainties from model parameters. Experimental data for the electric form factor $G^{p}_{\rm E}$ are taken from Refs. Gayou:2001qtJeffersonLabHallA:1999eplArrington:2007uxJeffersonLabHallA:2001qqeA1:2001xxyBatesFPP:1997rpw, and for the magnetic form factor $G^{p}_{\rm M}$ from Refs. Arrington:2004aeArrington:2007ux.
• Figure 4: Ratio of the proton’s Sachs FFs, $R_{p} = \mu_{p} G_{\rm E}^{p} / G_{\rm M}^{p}$. The black line shows the BLFQ prediction adopted from Ref. Xu:2024sjt, with the red band indicating uncertainties from the model parameters. Experimental data are taken from Refs. JeffersonLabHallA:2001qqeA1:2001xxyBatesFPP:1997rpwPunjabi:2005wqJeffersonLabHallA:2011yyiWalker:1993vjZhan:2011jiMacLachlan:2006vwPaolone:2010qc.
• Figure 5: Ratio of the proton Pauli to Dirac FFs. The lower panel shows the quantity $Q^2 F_2^p / (\kappa_p F_1^p)$, while the upper panel presents the scaled ratio $\left(Q^2 / \log^2[Q^2 / \Lambda_{\rm QCD}^2]\right) F_2^p / (\kappa_p F_1^p)$ for three values of the QCD scale parameter: $\Lambda_{\rm QCD} = 200$, 300, and 400 MeV. Here, $\kappa_p$ denotes the anomalous magnetic moment of the proton. Experimental data are taken from Refs. Gayou:2001qtJeffersonLabHallA:1999eplJeffersonLabHallA:2001qqePunjabi:2005wqPuckett:2010ac.